Sentence examples for using the integral formula from inspiring English sources

It is designed to calculate train state as accurate as possible by using the integral formula of dynamic equation.

Using the integral formula we prove that in top degree the former is isomorphic with the natural representation of W on coherent families of invariant eigendistributions and decomposes into a sum of the latter according to the decomposition of the nilpotent variety into G0-orbits.

Although the classical Moritz formula (Moritz 1980) was used to estimate DTE in the previous geoid model for Japan, here, we evaluated DTE using the integral formula of Martinec and Vaníček (1994b).

By contrast, the predicted result using the Integral formula showed the largest R2 value (= 0.93).

In particular, the predicted result using the Integral formula had the highest R2 value (= 0.93).

The current geoid model for Japan has been developed using the integral formulae of Martinec and Vaníček (1994a, b) for the computation of DTE and PITE.

Handling of the topographical effects on gravity was accomplished using the integral formulae of Martinec and Vaníček, which were found to be more suitable for geoid modeling over Japan than the classical formulae.

To prove the Hankel path, let us write the integrated function in the form of a power series in z and perform term-by-term integration using the integral representation formula for the reciprocal gamma function 1 Γ ( z ) = ∫ H a e ζ ζ z d ζ.

The far-field modal sound pressure is calculated first by using the Rayleigh integral formula and then obtained by treating the radiating surfaces as two cylindrical radiators.

Using the Cauchy integral formula, it is easy to show that hat{M}(lambda) = frac{1}{2pi i} int_{gamma} frac{hat{M}(mu )}{lambda- mu},dmu.

By using the Cauchy integral formula for the unbounded region Ω in Theorem 2, we have frac{1}{2pimathrm{i}} int_{Gamma}frac {g eta)}{eta-z},deta= left { textstylebegin{array}l@{quad}l} g z -g infty), & zinOmeg z -g infty), & zinOmegaega.